Titlebook: Chaos, Fractals, and Noise; Stochastic Aspects o Andrzej Lasota,Michael C. Mackey Textbook 1994Latest edition Springer Science+Business Med

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https://doi.org/10.1007/978-1-349-23334-2The preceding chapter was devoted to an examination of the various degrees of “chaotic” behavior (ergodicity, mixing, and exactness) that measure- preserving transformations may display. In particular, we saw the usefulness of the Koopman and Frobenius-Perron operators in answering these questions.

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https://doi.org/10.1007/978-1-349-23334-2In previous chapters we concentrated on discrete time systems because they offer a convenient way of introducing many concepts and techniques of importance in the study of irregular behaviors in model systems. Now we turn to a study of continuous time systems.

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Introduction,We begin by showing how densities may arise from the operation of a one- dimensional discrete time system and how the study of such systems can be facilitated by the use of densities.

LEER

油膏

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The Asymptotic Properties of Densities,The preceding chapter was devoted to an examination of the various degrees of “chaotic” behavior (ergodicity, mixing, and exactness) that measure- preserving transformations may display. In particular, we saw the usefulness of the Koopman and Frobenius-Perron operators in answering these questions.

認(rèn)識(shí)

Continuous Time Systems: An Introduction,In previous chapters we concentrated on discrete time systems because they offer a convenient way of introducing many concepts and techniques of importance in the study of irregular behaviors in model systems. Now we turn to a study of continuous time systems.

KEGEL

Pander

Modern Dance and the Modernist Work,e of the material developed in Chapter 5 Although results are often stated in terms of the asymptotic stability of {..}, where . is a Frobenius—Perron operator corresponding to a transformation ., remember that, according to Proposition 5.6.2, . is exact when {..} is asymptotically stable and . is m